Tuesday, July 16, 2024
HomeBaseballA Visible Primer on Horizontal Strategy Angle (HAA)

A Visible Primer on Horizontal Strategy Angle (HAA)


It’s been virtually two years since I authored a visible primer on vertical strategy angle (VAA) and virtually three years since I first mentioned VAA right here at FanGraphs. The subject immediately adjoining to VAA — horizontal strategy angle (HAA) — has been marinating in my thoughts (and in my drafts) ever since.

In an auspicious flip of destiny, whereas revisiting this draft, our beloved Eno Sarris reached out to ask if I had ever revealed something about HAA. He had questions on Brandon Pfaadt — particularly, Pfaadt’s sweeper. A lot was made about Pfaadt’s success this postseason, which might be attributed, in no small half, to his sweeper and the way he weaponized it. (Extra on that later.) I used to be spurred into motion. Thanks, Eno!

HAA: Like VAA, however Not as Cool

Simply as VAA captures the angle at which a pitch crosses dwelling plate vertically, HAA captures the identical horizontally. The pitcher’s launch level (the start of the pitch’s trajectory), the pitch’s remaining location (its finish), and the pitch’s velocity and acceleration vectors in all three dimensions in the end decide the pitch’s motion by house. This motion by house consists of the angles at which the pitch breaches the entrance airplane of dwelling plate. As a result of HAA is a perform of those different bodily descriptors, it correlates with them to various levels — and, due to this, can be type of obscured by them.

For VAA, I recommended adjusting it for vertical pitch location. VAA correlates so strongly with pitch top, it appeared virtually meaningless to me to quote uncooked VAA numbers. A -4.0 diploma VAA? Okay, however did the pitcher throw it on the high of the zone the place VAAs of -4.0 levels are commonplace, or did he throw it on the backside of the zone the place they virtually at all times aren’t? Like all issues baseball and sabermetric evaluation, context is essential.

Location is basically the complete extent of the changes wanted for VAA (that, and pitch kind, as a result of strategy angles fluctuate so extensively throughout pitch sorts). HAA is extra difficult. Like VAA, we’ll modify HAA for location, besides it’ll be horizontal pitch location, not vertical. It’s additionally crucial to normalize for:

  • Pitcher handedness: Horizontal motion patterns are distinctive to pitcher handedness, whereas vertical motion patterns are largely immune.
  • Horizontal launch level: A pitcher can fluctuate his horizontal launch level just by shifting his beginning place on the mound. If a pitcher throws two “similar” pitches to the very same goal from totally different ends of the rubber, they are going to naturally exhibit totally different HAAs. (Owen McGrattan mentioned this when he researched HAA two years in the past.) Except a pitcher stands on a crate or digs a gap within the mound, he can not alter his vertical launch level in the identical means with out dramatically affecting his arm slot and mechanics (and all of the pitch traits that end result from them).

In Chris Gilligan’s deep dive on Pfaadt, Postseason Hero, he famous that after Pfaadt was optioned and recalled, pitching coach Brent Strom and pitching guide Perry Husband labored with him to regulate his place on the rubber, shifting from the third-base aspect to the first-base aspect. Husband (appropriately) asserted that Pfaadt might change the looks — and, thus, the efficiency — of his pitches with out basically altering their shapes. Husband preached tunneling and efficient velocity. HAA doesn’t deal with these matters, at the least indirectly, but it surely rests adjoining to them: by shifting towards the first-base aspect of the rubber, Pfaadt augmented his HAAs and his efficiency.

Horizontal Strategy Angle Above Common (HAAAA)

Simply as I adjusted VAA for location to create VAAAA, I’ve adjusted HAA for location, handedness, and launch level inside every Statcast pitch kind classification to create Horizontal Strategy Angle Above Common, or “HAAAA.” Would “Adjusted HAA” have been higher? Possibly. Is HAAAA spectacularly uglier? Certain. Is it enjoyable to scream on the high of your lungs? Completely.

Each pitch kind can have a special league-average HAA worth (sliders and cutters have a lot sharper angles on common than sinkers or changeups), however they’ll all have HAAAAs that heart on zero, with “plus” or “minus” values to point above or beneath common for that pitch kind. To wit: listed beneath are 5 pitchers whose common HAAs are practically similar, each with each other and to the 2023 league common (1.3 levels, per my Pitch Leaderboard). HAA alone, one may misconstrue their four-seamers’ HAAs as similar to at least one one other and/or as “common” on advantage.

2023 4-Seamer HAA(AA)

SOURCE: Pitch Leaderboard

As you possibly can see, in adjusting for the distinctive combos of launch factors and areas (not on common however for all of the four-seamers they threw in 2023), HAAAA depicts these 5 choices as having considerably totally different strategy angle profiles.

Let’s Have a look at 4-Seamers First

Earlier than we proceed, please acquaint your self with these legends. These illustrations are offered from the catcher’s perspective.

As a result of we’re working with two laterally-oriented metrics — horizontal location and HAA — we’re burdened with forcing one in all them to adapt to the vertical Y-axis. HAA drew the brief straw. The farther up the Y-axis, the sharper the HAA towards left-handed hitters; the farther down, the sharper towards righties.

The third legend beneath synthesizes the primary two. Actually, I can’t let you know what number of occasions I’ve needed to refer again to this. It’s turning my mind to mush. I ought to have it tattooed on my forearm, or perhaps on the insides of my eyelids.

So far as color-coding is worried, purple means scorching and blue means chilly, in case you can imagine it. The metrics that underpin these warmth maps account for ball-strike rely. Swing charges on 0-0 are vastly totally different from swing charges with two strikes, for instance. Pitchers inadvertently create choice bias by utilizing totally different pitches (with various levels of high quality) in several conditions. It’s necessary to make sure we examine apples to apples. The depth of the warmth represents the magnitude of every metric above or beneath common, impartial of rely.


For pitchers throwing four-seamers towards hitters of the identical handedness (i.e., righties versus righties), sharper strategy angles towards the hitter correspond with greater swing charges on the within edge and decrease swing charges on the surface edge. Because the strategy angle shifts away from the hitter, swing charges drop inside and improve exterior.

I see two tendencies:

  1. Particularly on the edges of the zone, sharper HAAAAs beget extra exaggerated plate self-discipline outcomes; and
  2. Sharper HAAAAs afford themselves wider locational targets. For instance, a four-seamer with -0.6 diploma of HAAAA that’s situated a complete ball’s width off the within fringe of the plate will induce swings at a fee kind of commensurate with a median (+0.0 levels) four-seamer immediately on the black. That’s extra swings on would-be balls (and fewer swings on would-be strikes) for pitchers with sharper strategy angles.

Per MLB’s Mike Petriello, Strom stated this of Pfaadt throughout his occasions of turbulence:

“Earlier than, he was throwing balls out of his hand which grew to become strikes,” Strom stated in July. “Now we’ve pitches which are strikes that may develop into balls, which is what I used to be attempting to attain.”

That is good teaching! Regardless of tunneling, efficient velocity, and Strom’s/Husband’s different factors of focus, Strom leverages HAA in a significant means. He understands the worth of location and (once more, appropriately) implies that, by merely altering his launch level vis-à-vis his place on the rubber, Pfaadt can increase his sweeper’s efficiency with out altering his mechanics or the form of his pitch(es).

Within the absence of swings, we’ve non-swings that, relying on location, end in referred to as striks. The combos of strategy angle and placement that see fewer swings — sharper HAAAAs towards the hitter on the periphery — naturally produce extra referred to as strikes. Presumably these sharper strategy angles in these areas create the phantasm of a pitch that’s on a trajectory exterior the zone however cuts again in on the final second. Certainly, generally they really are, and it’s the umpire who has been fooled:

(I’ve lengthy thought this phenomenon, along with excessive VAAAAs on the high and backside of the zone, has implications for catcher framing — a dialogue for an additional day or a better thoughts than mine.)

By way of contact on swings, the farther inside, the more severe the hitter’s contact fee (higher for the pitcher, in purple), exhibiting a mild pattern in favor of sharp angles towards, inside over sharp angles away, exterior:

Flattening swings and speak to into one determine, we see normal favoritism for sharp strategy angles away from the hitter, even in weak areas like the middle of the zone:

Additional flattening every little thing into referred to as strikes plus whiffs (CSW), in the end the very best strategy is to seize referred to as strikes on the periphery with pitches breaking sharply towards from the hitter. This can be a handy and considerably intuitive end result: VAA(AA) is a swinging-strike weapon, HAA(AA) is a called-strike weapon.

This, in fact, focuses solely on plate self-discipline and neglects hitter contact high quality, which is an important part. When incorporating hitter contact high quality, we see just a few fascinating tendencies: the locational margin of error on the periphery is dramatically smaller, whereas it’s a lot wider inside. In truth, sharp strategy angles towards the hitter which are situated healthily inside are particularly efficient:

In different phrases, there’s a time and place for chasing strikes, particularly referred to as strikes, which come rather more simply than swinging strikes — however hitter batted ball outcomes are markedly inferior away from the areas the place these referred to as strikes come best. A minimum of for four-seamers, largely we see that extra intense HAAAAs don’t precisely translate to superior efficiency. There are obvious plate self-discipline good points with sharper HAAAAs, however they’re type of rendered inert by the volatility of batted ball occasions.

What About Non-Fastballs?

Quite than different pitch sorts individually, I merged all of them into one warmth map. We lose the granularity of every pitch kind’s quirks and nuances however obtain a broad understanding of strategy angles locationally — which, in the end, usually are not distinctly totally different from four-seamers anyway. Right here’s righties versus righties for all pitches:

As with four-seamers, the interior edge is king, particularly for pitches with ample arm-side. There are exaggerated results for ample glove-side minimize off the periphery, too, extra so from this all-pitch perspective than for four-seamers alone. Having the ability to generate above-average outcomes on pitches exterior the zone? That’s helpful! That margin of error for sweepy pitches off the periphery, nevertheless, is visibly smaller.

The warmth map towards left-handed hitters is successfully the identical, simply rotated 180 levels:

As a bonus, to carry it again to Pfaadt one final time, right here’s efficiency from righties towards all hitters for sweepers and sliders. There could also be some light bolstering results from sharper HAAAAs, however location prevails at the beginning.


A very powerful HAAAA results are proven for strategy angles breaking sharply towards the hitter on the surface edge (when it comes to CSW and referred to as strikes) and in addition on the within edge (when it comes to weak contact high quality). These good points can’t be realized with out pretty well-executed location, though, like VAAAA, excessive HAAAAs make command much less necessary. That, I believe, would help the argument for capital-‘s’ Stuff over command. However location is essential for HAAAA, arguably rather more so than for VAAAA.


By design, that is a very simplistic train. Binning and averaging, whereas loads illuminating in its personal proper, is wildly primitive in comparison with regression evaluation or machine studying. There are results proven right here that in a broader, extra rigorous evaluation may be proven to be over- or understated.

I have to additionally reiterate that this evaluation critically lacks the contextualizing advantages of many different pitch traits (Though HAA/AA does inherently account for velocity, acceleration, launch level, and placement. In its protection, that’s really quite a lot of issues.) Like every analysis effort in baseball, a person variable — on this case, HAAAA — ought to most likely by no means function a sole metric for evaluating a pitch. Let it complement or be supplemented.

Making the Changes to HAA

HAAAA reveals a lot smaller location-adjusted variations than VAAAA does. Whereas the the flattest (steepest) pitches might be as much as 1.5 levels and even 2.0 levels flatter (steeper) than the common pitch of their class, the runniest/sweepiest pitches hardly ever surpass 0.5 levels of extra HAA. It’s potential that if we modify HAA by one thing extra broadly outlined, like pitch class (“fastballs”) as a substitute of pitch kind (“four-seamers,” “sinkers”), then our magnitudes of HAAAA would really like improve. I’m unsure how rather more readability it could present us.

VAAAA is basically a weapon for fastballs however has use instances for different pitch sorts. HAAAA might have extra utility for breaking (and off-speed) pitches given their motion profiles. After I modify HAAAA for horizontal location (along with pitcher handedness and horizontal launch level), I accomplish that by pitch kind. I wish to know the way sharp a fastball’s strategy angle is in comparison with different fastballs. That’s doubtlessly not as useful for breaking pitches, not simply because breaking pitches fluctuate so extensively of their motion profiles but additionally as a result of breaking pitches now undertake so many various names and terminologies. And admittedly, that’s nice. I help that effort utterly. Name a pitch no matter you wish to name it to greatest describe its motion traits. However that makes it tough to check, for instance, sliders to sliders. A few of these sliders are referred to as sweepers now. A few of these sliders are referred to as sliders however are literally sweepers. A few of these sweepers are literally sliders. Some are slurves! And a few are tiny hamburgers. Who even is aware of anymore. Taxonomy is an actual subject, although, and it could constrain this evaluation (along with affecting the “changes” made on the premise of the aforementioned pitch kind classifications).

The Stuff-Versus-Command Wars

Accentuated HAAAAs can typically fail in dangerous areas the place VAAAAs may thrive. Why?

To me, the reason is pretty intuitive. A hitter’s swing has a a lot wider margin of error laterally than it does vertically. Horizontally, an inch off the barrel most likely nonetheless ends in contact, simply inferior contact. In truth, with a miss of a number of inches, a hitter can nonetheless foul one off and even luck right into a base hit. Alternatively, a one-inch miss vertically is, at greatest, a foul tip; at worse, it’s a straight-up whiff. And a whiff, on common, is unequivocally worse than inferior contact. This helps clarify not solely why elite VAAAAs (greater than elite HAAAAs) play up in dangerous areas, however why elite VAAAAs play up higher than elite HAAAAs typically.

Certainly, HAAAA stays depending on location. There’s a chicken-and-egg state of affairs right here. Stuff is a greater predictor of success, a lot to the chagrin of old-school sorts and innumerates. For HAAAA, although, stuff can’t exist with out command to some extent. It’s solely with some semblance of fine location — the strike zone’s edges, particularly — that HAAAA can play up. Even then, location shoulders most of that load. However good HAAAA-related stuff broadens the pitch goal, reduces the locational dependency, buys extra wiggle room. That’s, good HAAAA-related stuff elevates a command-oriented profile.

Pitch Modeling

Earlier than being employed to the Rockies’ R&D division, Ethan Moore wrote a seminal article on strategy angles. He present in modeling pitch traits that HAA demonstrated exorbitant run prevention results, though he admits “we’ve to take this with a grain of salt.” It’s potential that making use of changes to HAA (past together with location, launch level, and so on. as impartial variables within the mannequin) may yield a extra affordable (i.e., smaller) coefficient for HAA, particularly as HAAAA yields a a lot narrower distribution of potential values.


I apologize if I missed (and subsequently didn’t cite) your analysis on HAA. A cursory Google search of “horizontal strategy angle” turns up perhaps half a web page value of posts earlier than devolving again into posts about vertical strategy angle. I’ve seen people from Driveline and Tread evoke VAA and HAA on Twitter, however no analysis got here up. If I’ve missed something, please be at liberty to drop it within the feedback.

Editor’s word: Subsequent to publication, the graphics on this piece had been up to date to right an earlier error.



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